Controlling photothermoelectric directional photocurrents in graphene with over 400 GHz bandwidth

Photodetection in the near- and mid-infrared spectrum requires a suitable absorbing material able to meet the respective targets while ideally being cost-effective. Graphene, with its extraordinary optoelectronic properties, could provide a material basis simultaneously serving both regimes. The zero-band gap offers almost wavelength independent absorption which lead to photodetectors operating in the infrared spectrum. However, to keep noise low, a detection mechanism with fast and zero bias operation would be needed. Here, we show a self-powered graphene photodetector with a > 400 GHz frequency response. The device combines a metamaterial perfect absorber architecture with graphene, where asymmetric resonators induce photothermoelectric directional photocurrents within the graphene channel. A quasi-instantaneous response linked to the photothermoelectric effect is found. Typical drift/diffusion times optimization are not needed for a high-speed response. Our results demonstrate that these photothermoelectric directional photocurrents have the potential to outperform the bandwidth of many other graphene photodetectors and most conventional technologies.

(  ) = − ()  0 .Supplementary Equation (3) Here, the area charge density is () = Δ(  ), where   is the Fermi level, i.e. the level at 0  shifted by .We describe the carrier concentration as 2 =  0 2 + Δ 2 , where  0 the residual charge carrier concentration and Δ the induced carrier concentration.In this theoretical model, we set  0 = 0 for graphene and the above equation simplifies to () = (  ) . Combining Eq.S2 and S3 one obtains the charge density Next, we extract   and  directly from the resistance measurements provided in Fig. 2b.We follow a similar approach to ref 3 .We first convert the resistance to the conductivity (Supplementary Fig. 2a).The Dirac point conductivity corresponds to   = 0.172 .To calculate the mobility, we relate the gate voltage   to the Fermi level shift using the simulation results presented in Supplementary Fig.The mobility is then calculated with: and is found to be  0 ≈ 900  2 / close to the Dirac point.
Using all extracted values, the resulting Seebeck coefficient as a function of gate voltage is given Supplementary Fig. 3a.We also provide example curves in Supplementary Fig. 3b on how the Seebeck coefficient would be influenced if the carrier mobility would be improved (1'000, 2'000, 5'000, 10'000 and 20'000  2 /) Furthermore, the maximum Seebeck coefficient as a function of mobility and minimum conductivity is calculated in Supplementary Fig. 3c.Higher quality graphene (low   , high ) leads to an improved Seebeck coefficient whereas poor quality graphene (high   , low ) leads to a low value.The red square marks our values.We note that for this value the contact resistance is not removed.
Supplementary Fig. 3 The limitation is further visualized in Supplementary Fig. 5. Four cases are presented: Supplementary Fig. 5a,b present the 0° resonator orientation (i.e., baseline orientation) under 45° and 135° polarization excitation.Supplementary Fig. 5c,d present the 90° resonator orientation (i.e., crossbar orientation) for 0° and 90° polarization excitation.For each case, (1) represents the simulated optical field by showing the square of the electric field in the graphene layer.The mean value || 2 for a certain width (marked by a gray area) is extracted along the x-coordinate for each case and given in the cross-sectional view (2).The calculated Seebeck coefficient profile for one fixed gate voltage is provided in panel (3).The resulting force along the x-direction is calculated by   () =  * ()/ * |()| 2 , where  is used as a scaling factor.Panel (4) represents the force for each case Supplementary Fig. 5a through Supplementary Fig. 5d.Supplementary Fig. 5a,b show the photoresponse with its sign and also show a response of equal magnitude.Supplementary Fig. 5c can describe the 0° response, however, Supplementary Fig. 5d shows an   close to zero.The measured response, however, is clearly non-zero (Supplementary Fig. 4d).Therefore, the simple model can not fully describe the absorption and full hydrodynamic electron flow models as used in refs 4,5 are needed.They provide a more accurate view on the induced direction of the currents.• Lastly, the resistance difference between our device and the previous report is a factor 5.As photovoltages generated by the Seebeck effect are linked to thermoelectric currents across a PD by Ohms law the resistance has a direct influence on the current responsivity.This effect is seen also in Supplementary Fig. 15; The voltage responsivity divided by the current responsivity leads to ~3000 Ω matching the device resistance in the operation point.
Multiplying all estimated contributions leads to a total of ( . ) × ( ℎ) × (ℎ   ℎ) × ( ) 3  4  4  5 ~10 2 explaining the two order of magnitude lower current responsivity in our devices.At the same time, this also shows the unmet potential of this architecture -improving the graphene quality, moving to multilayer graphene and changing the resonator design could lead to responsivities close to, or even higher than 0.1 A/W.Furthermore, the responsivity can be increased by etching the graphene channel 5 .This would also increase the resistance and as a result could further reduce thermal noise and improve the NEP.However, for high-speed operation, it would cause a larger mismatch between the typically 50 Ω terminated RF-circuits and would lead to worse power transmission.Employing multilayer graphene would improve the current responsivity due to higher absorption and lower resulting resistance.Furthermore, saturation could potentially be increased.However, multilayer graphene will also have a lower mobility which in turn leads to a reduced Seebeck coefficient and therefore lower responsivity.The responsivity and detectivity will therefore improve up to a certain number of layers.Supplementary Fig. 16 provides simulated absorption spectra for different graphene layer thicknesses.In addition to the total absorption of the metamaterial layer stack, the absorption per medium is also shown.A clear boost in absorption in graphene is observed for an increasing amount of graphene layers.
Supplementary Fig. 16: Absorption per material of the architecture.Simulated absorption per material (rows) of the metamaterial absorber structure for different graphene thicknesses (columns).The first row shows the total absorption of the layer stack.The second row shows the absorption in the resonators consisting of gold and titanium.The third row shows the absorption in graphene which is strongly increasing with additional layers.Lastly, the fourth row shows the losses in the adhesion layer between the gold backplane and the alumina spacer layer.
Additionally, an overview of the state of the art of different graphene based PTE photodetectors is provided in the Supplementary Table 1.The table lists the graphene fabrication technology (exfoliated vs. photonic integrated circuit), the operation wavelength, the voltage responsivity, the maximum reported photovoltage and the bandwidth.
as a Neumann-type boundary condition (BC) in a general 3D PDE solver.The metallic resonators form a fixed potential Dirichlet BC and the gate electrode forms a controllable Dirichlet BC directly equal to the applied gate voltage   .Solving for the potential  as a function of position and applied gate voltage   , one arrives at the spatial potential distribution   (, ,   ).The results are provided in Supplementary Fig. 1.Supplementary Fig. 1: Graphene potential simulation.a Ferm level W F of a graphene sheet for a single unit cell of the metamaterial with 0 V applied gate.The metallic resonator dopes the graphene which also extends into the resonator.b Cross-section of the Fermi level along the black dotted line in a plotted across two unit cells.The different traces correspond to gate voltages V G from -3 V to 3 V in steps of 0.1 V. c Fermi level in the graphene away from the resonator (black dotted line in b) linking the gate voltage to the induced potential shift.
Fig. 2c) which allows to relate the measured conductivity to the carrier concentration (Fig S2d).

:
Resulting Seebeck Coefficient.a Seebeck coefficient as function of gate voltage (VG−VD, where VD is the Dirac voltage) for the extracted device parameters.b Calculated Seebeck coefficient for higher carrier mobility.c Seebeck coefficient as a function of carrier mobility and minimum conductivity.The red square marks the values from a.

Supplementary Fig. 7 :
Polarization dependent field and induced carrier flow behavior.Metamaterial resonators under different polarized excitations and the resulting || pattern (heatmap) and induced carrier flow.Rotating the polarization from 90° (see polar grid for orientation definition) to larger angles results in an asymmetric field distribution which starts to twist the flow upwards until it reaches 180° where the flow direction is weaker and reversed in comparison to the 90° case.Further turning the polarization beyond 180° twists the flow downwards until it rotates back to the initial flow direction for the 90° / 270° polarization.

Table 1 : Comparison of graphene based PTE photodetectors sorted by publication year
. "Fab" stands for the fabrication method of the graphene sheet (Ex.-mechanical exfoliation, CVD -chemical vapor deposition)."Int."stands for integration scheme (PIC -photonic integrated circuit, FS -free space illuminated).λ is the illumination wavelength in nanometer.ℛ V is the reported voltage responsivity.V max is the maximum reported photovoltage signal.The last column summarizes the reported bandwidths (BW) of the devices.The larger than ">" symbol denotes setup limited bandwidths.